5.4.4 Boundary Conditions

The boundary conditions at the six sides of the computational box
cannot be specified independently.
For the naming convention of the boundaries a gravitational acceleration
in -x3 direction is assumed.
Accordingly, there is a bottom and a top boundary, and four side boundaries.

All boundary conditions of the hydrodynamic case are available in the MHD module.

character side_bound:
The boundary condition at all four sides is given by e.g.

Any of these values can be specified. But in fact, not all of them are recognized by all
modules. Therefore some parameters are for test purposes (e.g. shock calculations) only.
In simulations of a solar-like star with the MSrad radiation transport module
the side boundaries have to be periodic.
In simulations of a red supergiant all boundaries (including the sides) will typically
be transmitting. As an alternative, closed boundaries can be chosen in this case.

character top_bound:
The boundary condition at the top of the model is given by for instance

In almost every simulation of stellar convection a transmitting top
boundary will be selected, the closed one is an alternative.
The periodic condition is only recognized by the hydrodynamics routines
and not by any radiation transport routine.

character bottom_bound:
The boundary condition at the bottom of the model is given for instance by

closedbottom2: closed wall, handles gravity, radiation in diffusion approximation.
In this version, the extrapolation of quantities should be smoother than for
closedbottom.

periodic: periodic boundaries for hydrodynamics, radiation.

transmitting: transmitting boundary for hydro and outward radiation.
The parameters real c_tchange, real c_tsurf, and
real c_hptopfactor have to be specified.

inoutflow: "classical" open lower boundary for deep convection,
gravity and radiation possible.
The parameters real s_inflow, real c_schange, and
real c_pchange have to be specified.

inoutflow2: variant of the open lower boundary condition.
The parameters real s_inflow, real c_schange,
real c_pchange have to be specified.
In this version, the extrapolation of quantities should be smoother than for
inoutflow.

In simulations of a solar-like star with the MSrad radiation transport module
the bottom boundary is typically of type ``inoutflow''.
A supergiant simulation will have a transmitting lower boundary.

character heat_mode:
The mode in which energy is supplied can be adjusted with this parameter.
The classical choice is to leave it empty, in which case the mode is
chosen from s_inflow (see Sect. 5.4.4) and
luminositypervolume (see Sect. 5.4.4).
Example:

: (empty). The classical value.
For local models the energy comes through the lower boundary,
either by radiation (for a closed bottom boundary closedbottom)
or by convection + radiation (for an open bottom boundary inoutflow).

bottom_entropy1: The entropy in the bottom layers (defined as being less than
r0_grav above the bottom of the model) is adjusted towards
s_inflow on a rate given by c_schange.

bottom_energy1: Energy in the bottom layers is added according to
luminositypervolume.

real luminositypervolume:
The luminosity of a ``Star-in-a-Box''
or a local model with the appropriate heat_mode
can be set with this parameter.
To avoid numbers that do not fit into a 4 Byte real the luminosity per volume
has to be specified as e.g. in

In the case of a central potential the entropy in a sphere with radius
r0_grav is adjusted towards this entropy value.
In both geometry (supergiant as well as solar) this value is very important as
it finally (but indirectly) determines the luminosity and
effective temperature of the star.
A value of 0.0 (default) or below disables this energy input.

real c_schange:
The entropy s_inflow of the material in the bottom layer
(solar case, inoutflow boundary condition)
or the central region of the model (supergiant case) is not just
set to the specified but adjusted towards it. The adjustment rate can be
controlled with e.g.

real c_pchange:
The inoutflow boundary condition not only controls entropy and velocity
but also the pressure in the bottom layers:
It is locally adjusted towards the global average to damp out possible
instabilities.
The adjustment rate can be specified e.g. with

real c_rhochangetop:
The transmitting upper boundary condition
can smooth density fluctuations with this parameter.
It is locally adjusted towards the global average to damp out possible
instabilities. It appears to be useful for the HLLMHD solver.
For simulations without magnetic fields, there is no need to set this parameter, so far.
The adjustment rate can be specified e.g. with

real c_tsurf:
In the case of a transmitting upper or outer boundary
the temperature of the material streaming into the model
is adjusted towards a temperature teff*c_tsurf.
This temperature can be specified as fraction of the effective temperature
e.g. with

The value depends on where the outer boundary is located relative to
the photosphere:
If the boundary lies at a point where the solar photospheric minimum temperature
is located, it can be fairly small.
If the boundary is far away from the photosphere of a red supergiant,
the value can be even smaller.
On the other hand, if the boundary lies somewhere within the solar chromosphere
even values above 1.0 might be reasonable.

real c_hptopfactor:
In the case of a transmitting upper or outer boundary
the density stratification outside the model has to be extrapolated properly.
Assumptions about this density affects the amount of mass flowing
into the model.
For the extrapolation it is assumed that the density scale scales
with the pressure scale height as
=/c_hptopfactor.

0.0 C 1.0: The density scale height is enlarged to account for
possible effects of turbulent pressure on the scale height:
The density decays less rapidly with height than in
an (isothermal) hydrostatic stratification.

real rho_min:
During long periods of matter infall the density at an open outer boundary can
become very low. To limit the decrease of the density a lower limit in the extrapolated
ghost cells can be set e.g. with

The density within the model will typically not fall much below this value.
A value of 0.0 (default) or below deactivates this feature.

real c_coredrag:
To damp the flow in the core of models with central potential
a drag force restricted to the inner part of the model
(r0_grav)
can be applied.
It is controlled e.g. with

real c_coredrag f=E15.8 b=4 n='Core drag force parameter' u=1
1.0

A value of 0.0 (default) or below deactivates this feature.

The following parameters are specific to MHD simulations. For MHD calculations
they must be set additional to the hydrodynamic boundary parameters.

character side_bound_mag_x1 and character side_bound_mag_x2:
The boundary condition at the sides perpendicular to the x1 direction and
perpendicular to the x2 direction, respectively. They are given by e.g.

constant: constant extrapolation of all magnetic field components into the ghost cells.

periodic: periodic continuation of all magnetic field components into the ghost cells.

fixed: the component normal to the boundary is kept fixed at its inital value.
Constant extrapolation applies for the transversal components.

vertical: constant extrapolation for the vertical component.
The transversal cell-centered field is mirrored, with the opposite sign.
That should result in transversal components of the boundary-centered field being zero at the boundary.

vertical2: constant extrapolation for the vertical component.
The transversal cell-centered field is set to zero.

reflective: The magnetic field is mirrored at the boundary.
This boundary condition is unphysical, because the magnetic field
is an axial vector and because it violates the divergence free property of the
magnetic field. Therefore, this boundary condition should be used with caution.

The fixed conditions are realized by setting the electric field at those cell edges that
coincide with the physical boundary zero. This is done in the constrained transport module.

character top_bound_mag:
The boundary condition at the top of the model is given by for instance

constant: constant extrapolation of all magnetic field components into the ghost cells.

periodic: periodic continuation of all magnetic field components into the ghost cells.

fixed: the component normal to the boundary is kept fixed at its inital value.
Constant extrapolation applies for the transversal components.

vertical: constant extrapolation for the vertical component.
The transversal cell-centered field is mirrored, with the opposite sign.
That should result in transversal components of the boundary-centered field being zero at the boundary.

vertical2: constant extrapolation for the vertical component.
The transversal cell-centered field is set to zero.

oblique: magnetic fields with a given inclination at the boundary. The inclination
is specified through parameters C_magthetaB and C_magphiB.

character bottom_bound_mag:
The boundary condition at the bottom of the model is given by for instance

constant: constant extrapolation of all magnetic field components into the ghost cells.

periodic: periodic continuation of all magnetic field components into the ghost cells.

fixed: the component normal to the boundary is kept fixed at its inital value.
Constant extrapolation applies for the transversal components.

vertical: constant extrapolation for the vertical component.
The transversal cell-centered field is mirrored, with the opposite sign.
That should result in transversal components of the boundary-centered field being zero at the boundary.

vertical2: constant extrapolation for the vertical component.
The transversal cell-centered field is set to zero.

oblique: magnetic fields with a given inclination at the boundary. The inclination
is specified through parameters C_magthetaB and C_magphiB.

inoutflow: magnetic field can be advected into the computational domain by ascending material flow.
Its strength can be specified with the parameter b1_inflow. The boundary condition
for the hydrodynamic variables must be set to inoutflow too, otherwise this boundary
condition is the same like constant.

In the case of inoutflow the magnetic field, which is advected into the computational domain
has a unique component which is in the x1 direction and it is only present where a velocity in
the positive x3 direction exists. In all other places, the magnetic field components are constantly
extrapolated into the ghost cells.

real b1_inflow:
This parameter controls the strength of the inflowing horizontal magnetic field
at the lower boundary in connection with bottom_bound_mag=inoutflow.
The default value is 0.0.
Example:

real C_magphiB:
This parameter specifies the angle between the horizontal component of the
magnetic field vector and the x1-axis (in radians) in the case of
oblique boundary conditions. The default value is 0.0.
Example: